In this exercise we work with the Black- Scholes setting applied to foreign currency denominated assets. We will see a different use of Girsanov theorem. [For more details see Musiela and Rutkowski (1997).] Let r, f denote the domestic and the foreign risk-free rates. Let St be the exchange rate, that is, the price of one unit of foreign currency in terms of domestic currency. Assume a geometric process for the dynamics of St:
dSt = (r ˆ’ f )Stdt + σStdWt
(a) Show that

Where Wt is aWiener process under probability P.
(b) Is the process

a martingale under measure P?
(c) Let Q be the probability

What does Girsanov theorem imply about the process, Wt ˆ’ σt, under Q?
(d) Show, using Ito formula, that

where Zt = 1/St.
(e) Under which probability is the process Ztert/eft a martingale?
(f) Can we say that Q is the arbitrage-free measure of the foreign economy?

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